0.1 Brief Description

In my study I looked at oviductal egg retention, the ability to retain eggs within the oviduct while development is halted, in freshwater turtles. I was interested in seeing cost benefit of retaining eggs for extended period of time verses a different form of parental care. To study this I looked at the cost of egg retention by measuring Eastern Musk Turtles metabolic rates using flow through respirometry.

gravidfemale Eastern Musk Turle

0.2 Adjusting for Egg Metabolism

Before we can run any tests we need to calculate energy produced during the respirometry run we need to convert our mL CO2/hr into joules/hr using conversion factors. The conversion factors were taken from Gessaman and Nagey 1988 and Reid et al 2009.

Data

Below is a description of all the factor variables included within my data set.

Turtle_ID: 54 total individuals

Group: Gravid Females, Males, Non-Gravid Females

mlCO2/hr turtles: measured metabolic rates

Turtle_Mass: Individual turtle mass to the nearest gram

mlO2/min eggs: measured metabolic rates for whole clutch of eggs

Whole clutch mass: reported weigths(g) of the entire clutch for each gravid female

mlO2/hr eggs: measured metabolic rates for whole clutch of eggs

Joules/hr turtles: calculated joules per hour used my indivudal turtles using the conversion factor

Joules/hr whole clutch: calculated joules per hour used by the whole clutch from each gravid female

adj_energy_joules_turtles: subtracting the joules/hr for the clutch from each of the gravid females

Fig 2 A linear plot showing joules/hr of energy produced during a 48 hour respirometry run for gravid females(blue), males(yellow), and non-gravid females.

All turtles have a positive correlation in metabolic rates (joules/hr) while accounting for the adjusted turtle mass (subtracting the gravid female’s clutch mass from her mass in order to get the actual mass of the female). From the graph it looks as though gravid females have a higher metabolic rate then do males and non-gravid females for the the reproductive season. We will run an ANCOVA with a pairwise test to determine if this is the case for these turtles.

Before running an ANCOVA and a pairwise test I ran the an autoplot to check for potential outliers. Here we see in the normal Q-Q plot that three values (16,15,36) could be potential outliers, however, they do not seem to deviate from the line too much so they may be okay.The first and third plot do not show any signficant pattern which is good.

##Autoplot

0.3 ANCOVA/Adjusted Means

Table 1. A summary kable displaying ANOVA summary table.
Df Sum Sq Mean Sq F value Pr(>F)
adj_mass_turtles 1 9959.259 9959.2592 24.587475 1.06e-05
Group 2 6550.128 3275.0639 8.085496 1.00e-03
Residuals 45 18227.437 405.0542 NA NA

The ANCOVA results support the linear plot above in that group (gravid female, male, non-gravid female) is signficant in determing metabolic rates of the indivdual turtle.The adjusted mass also was signficantly correlated with metabolic rates of the turtles (joules/hr) with a p-value< 0.05.

In order to adjust for the difference in mass of the three groups of turtles we need to use the package library(emmeans) to run our model.

kable(adj_turtles_1, format = "pandoc", caption ='Table 2. A summary kable displaying emmeans (adjusted means).')
Table 2. A summary kable displaying emmeans (adjusted means).
adj_mass_turtles Group emmean SE df lower.CL upper.CL
118.3061 Gravid Female 103.38249 5.610592 45 92.08218 114.68280
118.3061 Male 83.00421 4.761099 45 73.41487 92.59356
118.3061 Non-Gravid Female 74.09288 4.743735 45 64.53851 83.64725

After adjusting for the means of the metabolic rates we can now run a pairwise analysis. Here we see that we get a signficant diffence between gravid females and males (p-value-0.022). A signficant difference is also seen between gravid females and non-gravid females (p-value=0.001). A nonsignficant difference is reported when looking at males and non-gravid females (p-value=0.388).

Table 3. A summary kable displaying pairwise analysis.
contrast estimate SE df t.ratio p.value
118.30612244898,Gravid Female - 118.30612244898,Male 20.38 7.39 45 2.76 0.022
118.30612244898,Gravid Female - 118.30612244898,Non-Gravid Female 29.29 7.35 45 3.99 0.001
118.30612244898,Male - 118.30612244898,Non-Gravid Female 8.91 6.72 45 1.33 0.388

On a pairwise basis after adjusting for mass we find that their is a signficant difference between gravid female energy expenditure verses both male and non-gravid female energy expenditure (p-value< 0.05). There was no signficant difference found between males and non-gravid females (p-value= 0.3887).

##Gravid Females Only

0.4 Linear Regression Analysis

attach(adj_metabolic_rate)
library(ggpubr)
## Loading required package: magrittr
## 
## Attaching package: 'magrittr'
## The following object is masked from 'package:tidyr':
## 
##     extract
ggarrange(clutch_mass,clutch_mass_2,egg_number, sterno_mass, ncol = 2, nrow =2, labels = c("A", "B", "C","D"))

Fig. 3Linear regression analysis was run to determine if whole clutch mass(figure B), clutch size(figure C), whole clutch metabolic rate (figure A), or female body mass (figure D) significantly correlated with total cost of egg retention (adjusted metabolic rate – non-gravid metabolic rate).

## 
## Call:
## lm(formula = Joules_hr_eggs ~ whole_clutch_mass, data = adj_metabolic_rate)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1277 -0.0720  0.0219  0.0450  0.1552 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)  
## (Intercept)        0.06486    0.10520    0.62     0.55  
## whole_clutch_mass  0.01701    0.00738    2.30     0.04 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0867 on 12 degrees of freedom
## Multiple R-squared:  0.307,  Adjusted R-squared:  0.249 
## F-statistic: 5.31 on 1 and 12 DF,  p-value: 0.0399
## 
## Call:
## lm(formula = adj_energy ~ whole_clutch_mass, data = adj_metabolic_rate)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -20.53  -7.51  -1.41   7.42  21.89 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          -6.43      15.64   -0.41    0.688  
## whole_clutch_mass     2.88       1.10    2.62    0.022 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.9 on 12 degrees of freedom
## Multiple R-squared:  0.364,  Adjusted R-squared:  0.311 
## F-statistic: 6.86 on 1 and 12 DF,  p-value: 0.0224
## 
## Call:
## lm(formula = adj_energy ~ clutch_size, data = adj_metabolic_rate)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -23.534  -7.087  -0.567  10.215  23.561 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)    10.83      16.00    0.68     0.51
## clutch_size     5.89       4.02    1.47     0.17
## 
## Residual standard error: 14.9 on 12 degrees of freedom
## Multiple R-squared:  0.152,  Adjusted R-squared:  0.0811 
## F-statistic: 2.15 on 1 and 12 DF,  p-value: 0.169
## 
## Call:
## lm(formula = adj_energy ~ adj_mass, data = adj_metabolic_rate)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -20.98 -13.59   3.85   9.81  19.11 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)    2.408     22.799    0.11     0.92
## adj_mass       0.256      0.184    1.39     0.19
## 
## Residual standard error: 15 on 12 degrees of freedom
## Multiple R-squared:  0.138,  Adjusted R-squared:  0.0664 
## F-statistic: 1.92 on 1 and 12 DF,  p-value: 0.191

After running the linear models on each of the figures(A-D) we see that only whole clutch mass and whole clutch metabolic rate have a signficant positive correlation with metabolic rates.

We can run a multi linear regression model and see that we get the same answer that clutch size and female body mass is non-signficant for female metabolic rates.

Figure 4 There are two that appear to have some collinearity, however, this is not a problem because they are showing the same thing. One of the variables is just the adjusted for clutch metabolic rates.

## Warning in formals(fun): argument is not a function
## Fixed term is "(Intercept)"
importance(results)
##                      whole_clutch_mass Joules_hr_eggs clutch_size adj_mass
## Sum of weights:      0.54              0.44           0.16        0.16    
## N containing models:    8                 8              8           8

Again we see that whole clutch mass and egg metabolic rates are the most important factors to consider when looking at gravid female metabolic rates.

0.5 Gravid vs. Non-gravid Metabolic Rates

library(ggpubr)
ggarrange(plot_SMR2,line, nrow =2, labels = c("A", "B"))

Fig. 5 The top linear plot(A) is showing the metabolic rates of each gravid females metabolic rate with her non-gravid metabolic rate plotted below it. The second plot (B) is showing each females average metabolic rate prior to oviposition ( before laying her eggs) and then her metabolic rate after she has nested (post-oviposition)

From figure 4 you can see that a gravid females metabolic rate is almost twenty percent higher than he non-gravid metabolic rate. This supports the idea that gravid females are investing some energy into oviductal egg retention. This may not be as signficant of an investmant than would vitellogensis or other parts of the reproductive cycle.

I also ran an ANOVA/pairwise analysis to just specifically look at each gravid females gravid metabolic rate and her non-gravid metabolic rate.

Table 1. A summary kable displaying group, adjusted means, lower and upper smr rates.
adj_Mass Status emmean SE df lower.CL upper.CL
124 Gravid 106.1 4.14 23 97.5 114.6
124 Non_Gravid 73.2 4.14 23 64.6 81.8 
pairs(adj_turtles)
##  contrast                        estimate   SE df t.ratio p.value
##  124.5,Gravid - 124.5,Non_Gravid     32.9 5.85 23 5.620   <.0001

As is supported by the graph a gravid females metabolic rate is signficantly higher than non-gravid females metabolic rate (p-value=0.001).